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Find the stationary points of the graph x^3 + y^3 = 3xy +35

Differentiate wrt x to get 3x 2 + 3y 2 dy/dx = 3y + 3x dy/dx Rearrange to get dy/dx = (3x 2 - 3y)/(3x-3y 2 ). Set dy/dx =0 and infer y=x 2 . Substitute in for y into original equation and rearrange to get x ...
JB
Answered by Joe B. • Maths tutor
10495 Views

Solve the equation 10x + 4 = 12x + 2

2 = 2xTherefore x = 1
ZY
Answered by Zain Y. • Maths tutor
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Triangle ABC has perimeter 20 cm. AB = 7 cm. BC = 4 cm. By calculation, deduce whether triangle ABC is a right-angled triangle.

This is a question I recently tackled with one of my tutees from the edexcel GCSE specimen papers. I would begin to tackle any geometry question like this by drawing the triangle in question. We are given th...
CH
Answered by Carter H. • Maths tutor
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What is the gradient of a line with the equation y=4x+5?

The Gradient is 4, this is because this is a straight line graph and it is in the form of y=mx+c, with m being the gradient and c being the y intercept. If the equation was y=6x+3, the gradient would be 6. W...
TM
Answered by Tom M. • Maths tutor
14204 Views

Differentiate y=ln(x)+5x^2, and give the equation of the tangent at the point x=1

First differentiate the equation, giving you, y'=(1/x)+10x. To get the gradient at this point of the curve, plug in x=1, to get a y' value of 11, and a y value of 5. From there you can plug these three numbe...
HM
Answered by Harrison M. • Maths tutor
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